What's the main difference between Pohlig-Hellman and RSA?

Question

Both Pohlig-Hellman and RSA perform encryption and decryption by exponentiation modulo some integer ($p$ prime for PH, $n$ composite for RSA). They both use a key $e$ as the exponent to encrypt a message. They both use the inverse element of key $e$ to decrypt. In both, the encryption key $e$ can be a randomly chosen integer coprime with $p-1=\phi(p)$ (for PH) or $\phi(n)$ (for RSA).

So what's the main difference between Pohlig-Hellman and RSA?

^{Note: The question has been edited for accuracy and more standard notations.}

Answer 1

The main difference is that Pohlig-Hellman is a symmetric cypher, while RSA is a public key system. This is because, with Pohlig-Hellman, anyone who knows the encryption key $e$ can compute the inverse operation (because the 'decryption' key $e^{-1} \bmod p-1$ is easy to compute), while the RSA, someone who knows the encryption key $e$ (but not the factorization of the RSA modulus) cannot compute the decryption operation.